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Results tagged with integer-sequences
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user 5263
For questions about sequences of integers. References are often made to the online resource oeis.org.
5
votes
On vanishing of $p$-adic logarithms
The $p$-adic logarithm can be computed
$$
\begin{align*}
\log_p(2) &= \frac{1}{p-1}\log_p(2^{p-1})\\
&=\frac{1}{p-1}\sum_{n\geq 1}(-1)^{n-1} \frac{(2^{p-1}-1)^n}{n} \\
&\equiv -pF(p)\mod p^2.
\end{ali …
- 9,061
22
votes
Accepted
Is every sequence that looks like an AP really an AP?
For each $n$, the differences $a_{n+1}-a_n$, $a_{n+2}-a_{n+1}$, and $a_{n+2}-a_n$ can only be divisible by powers of $2$ and primes less than or equal to $c$. Since
$$
\frac{a_{n+2}-a_{n+1}}{a_{n+2}- …
- 9,061
4
votes
Sequences with integral means
Here are some bounds on the stable value $r(n)$, as well as the number of terms of the sequence that need to be calculated. The short version is that
$$
\frac{\sqrt{2}}{2}\sqrt{n}+O(1)\leq r(n)\leq \f …
- 9,061